Positronium formation in the excited state in the presence of a laser field

A straightforward approach for the evaluation of the rearrangement scattering amplitude in the first Born approximation has been given for the study of positronium (Ps) formation in the first excited state (n = 2) in e(+)-H(1S) collisions in the presence of a homogeneous, single mode, linearly polarized laser field embodying the full interaction potential. The projectile-laser-field interaction and the dressing effects on the target hydrogen atom and the Ps atom in the final channel have been considered to first order. The A . p gauge has been adopted in constructing the dressed wave functions. The FBA scattering amplitudes have been obtained in closed analytic forms for field direction parallel to the incident positron momentum. The differential cross sections for Ps (n = 2) formation have been presented for no photon and one photon exchange (l = 0, +/- 1) at 50, 100 and 200 eV energies with laser field amplitude epsilon(o) = 1.0 x 10(8) V cm(-1) and the angular frequency <(h)over bar omega> = 1.17 eV. The relations between the differential cross sections and the laser field strength, angular frequency and incident energy have also been demonstrated.